Psi and Phi Angles

A tetrapeptide, such as Leu-Leu-Ile-Tyr, contains four amino acids connected together with three amide or peptide bonds. Since an amide bond has pi bond character, the six atoms that constitute a peptide bond all lie in the same plane - the orange plane is the peptide bond connecting Tyr and Ile and the yellow one connects Ile and Leu. As with any peptide the conformation of the backbone is determined by the values of two torsional angles - psi (&psi;) and phi (&phi;) of each interior amino acid.

Determining values for psi (&psi;) and phi (&phi;)
The four atoms which constitute a &psi; are an amide nitrogen, a carbonyl carbon, an &alpha;-carbon and a second nitrogen. After toggling off spin and rotating the structure so that you can clearly see that you are not clicking on a transparent atom, determine and display the numerical value of &psi; by double clicking on a nitrogen of the angle, single clicking on the next two atoms and then double clicking on the second nitrogen. (If the structure rotates in the course of clicking on the atoms or if you encounter some other problem, re-click on the green link 'four atoms' and restart clicking on the atoms.) The four atoms making up &phi; are a carbonyl carbon, the connecting &alpha;-carbon, an amide nitrogen and the next carbonyl carbon (all marked with green halos). After rotating the structure so that the four atoms can be clearly seen, measure and display the numerical value of &phi; using the technique described above. Confirm the direction of rotation and the values of &psi; and &phi;.

Draw the planes of two other peptide bonds, and then using the technique described above identify the atoms contained in and the numerical values of the &psi; and &phi; angles of the &alpha;-carbon connected to these two planes. Confirm that you obtain the correct values.

More Detail on Psi and Phi
The initial scene shows psi and phi values for Ile. Notice the three colored triangular planes. The yellow plane serves as the references in measuring the two angles. The purple plane is part of the planar peptide bond (side chains removed for clearer viewing) between Tyr and Ile (red plane), and the angle between the red and yellow planes is psi. The orange plane is part of the planar peptide bond between Ile and Leu (blue plane), and the angle between the blue and yellow planes is phi. An amino acid needs to be bonded to two other amino acids in order to have values set for both psi and phi, for that reason the two terminal amino acids do not have values set for these angles. Show psi/phi for both Ile and Leu47. Notice that the orange plane involved in setting phi = -149o is in the same peptide bond plane as the purple plane that sets psi for Leu at -34o. With this being the case the psi for Leu47 can not be set by rotating this peptide bond plane because in doing so the Ile phi value would change. The alpha carbon and its bonded atoms (larger diameter sticks) can be rotated to set psi for Leu47. Since the carbonyl carbon does not leave the plane of the peptide bond, the rotation of the &alpha;-carbon changes the angle of the yellow plane relative to the plane of the peptide bond (orange and purple), and thus sets the the psi for Leu47. The phi for Leu47 is set by rotating the red plane (plane of the Leu46-Leu47 peptide bond). Show overlay with second peptide (original peptide - green chain and second peptide - red chain). The second peptide has an identical sequence, but the Ile has phi = -49o rather than -149o, and the peptides were overlaid so that the Tyr and Ile of the two peptides overlay each other. The peptides diverge at the carbonyl group of Leu47, the yellow reference planes of the two peptides occupy the same space, and therefore since the phi values are different the orange planes are in different locations. The remainder of the peptide chains do not overlay, even though the <scene name='Psi_and_Phi_Angles/Both_model_ile_leu_angles/1'>psi and phi of Leu47 are the same in both peptides.

Displaying Psi and Phi Values
The values for these two angles can be determined for the residue of any protein entry in Proteopedia by doing the following:
 * In the Jmol applet showing the 3D structure, click on the Jmol logo (or frank) in the bottom right corner.
 * When the menu comes up, select Console.
 * Click in the lower text box of the console that comes up, type the Select command followed by the number of the residue (Obtain this number in the Jmol applet by hovering over the residue whose psi and phi you want to determine), a ";" and the command draw rama and then press the Return key.